arXiv subjects

David L. Feder

Publications and source records attributed to David L. Feder.

35 records · Page 2Linked to original sources

arXiv2011

Strategies for measurement-based quantum computation with cluster states transformed by stochastic local operations and classical communication

We examine cluster states transformed by stochastic local operations and classical communication, as a resource for deterministic universal computation driven strictly by projective measurements. We identify circumstances under which such states in one dimension constitute resources for random length single-qubit rotations, in one case quasi-deterministically (N-U-N states) and in another probabilistically (B-U-B states). In contrast to the cluster states, the N-U-N states exhibit spin correlation functions that decay exponentially with distance, while the B-U-B states can be arbitrarily locally pure. A two-dimensional square N-U-N lattice is a universal resource for quasideterministic measurement-based quantum computation. Measurements on cubic B-U-B states yield two-dimensional cluster states with bond defects, whose connectivity exceeds the percolation threshold for a critical value of the local purity.

quant-ph↗

arXiv2011

Edge local complementation for logical cluster states

A method is presented for the implementation of edge local complementation in graph states, based on the application of two Hadamard operations and a single controlled-phase (CZ) gate. As an application, we demonstrate an efficient scheme to construct a one-dimensional logical cluster state based on the five-qubit quantum error-correcting code, using a sequence of edge local complementations. A single physical CZ operation, together with local operations, is sufficient to create a logical CZ operation between two logical qubits. The same construction can be used to generate any encoded graph state. This approach in concatenation may allow one to create a hierarchical quantum network for quantum information tasks.

quant-ph↗

arXiv2010

Universal quantum computation by discontinuous quantum walk

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantum computation in which a quantum walker takes discrete steps of continuous evolution. This `discontinuous' quantum walk employs perfect quantum state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, thereby ensuring unitary evolution without requiring the introduction of an ancillary coin space. The run time is linear in the number of simulated qubits and gates. The scheme allows multiple runs of the algorithm to be executed almost simultaneously by starting walkers one timestep apart.

quant-ph↗

arXiv2010

Testing equivalence of pure quantum states and graph states under SLOCC

A set of necessary and sufficient conditions are derived for the equivalence of an arbitrary pure state and a graph state on n qubits under stochastic local operations and classical communication (SLOCC), using the stabilizer formalism. Because all stabilizer states are equivalent to a graph state by local unitary transformations, these conditions constitute a classical algorithm for the determination of SLOCC-equivalence of pure states and stabilizer states. This algorithm provides a distinct advantage over the direct solution of the SLOCC-equivalence condition for an unknown invertible local operator S, as it usually allows for easy detection of states that are not SLOCC-equivalent to graph states.

quant-ph↗

arXiv2009

Error-correcting one-way quantum computation with global entangling gates

We present an approach to one-way quantum computation (1WQC) that can compensate for single-qubit errors, by encoding the logical information residing on physical qubits into five-qubit error-correcting code states. A logical two-qubit cluster state that is the fundamental resource for encoded quantum teleportation is then described by a graph state containing ten vertices with constant degree seven. Universal 1WQC that incorporates error correction requires only multiple copies of this logical two-qubit state and a logical four-qubit linear cluster state, which are prepared only just in advance of their use in order to minimize the accumulation of errors. We suggest how to implement this approach in systems characterized by qubits in regular two-dimensional lattices for which entangling gates are generically global operations, such as atoms in optical lattices, quantum dots, or superconducting qubits.

quant-ph↗

arXiv2009

Topological Entropy of Quantum Hall States in Rotating Bose Gases

Through exact numerical diagonalization, the von Neumann entropy is calculated for the Laughlin and Pfaffian quantum Hall states in rotating interacting Bose gases at zero temperature in the lowest Landau level limit. The particles comprising the states are indistinguishable, so the required spatial bipartitioning is effected by tracing over a subset of single-particle orbitals. The topological entropy is then extracted through a finite-size scaling analysis. The results for the Laughlin and the Pfaffian states agree with the expected values of $\ln\sqrt{2}$ and $\ln\sqrt{4}$, respectively.

cond-mat.mes-hall↗

arXiv2008

Cooling ultracold bosons in optical lattices by spectral transform

It is shown theoretically how to directly obtain the energy distribution of a weakly interacting gas of bosons confined in an optical lattice in the tight-binding limit. This is accomplished by adding a linear potential to a suitably prepared lattice, and allowing the gas to evolve under the influence of the total potential. After a prescribed time, a spectral transform is effected where each (highly non-local) energy state is transformed into a distinct site of the lattice, thus allowing the energy distribution to be (non-destructively) imaged in real space. Evolving for twice the time returns the atoms to their initial state. The results suggest efficient methods to both measure the temperature in situ, as well as to cool atoms within the lattice: after applying the spectral transform one simply needs to remove atoms from all but a few lattice sites. Using exact numerical calculations, the effects of interactions and errors in the application of the lattice are examined.

cond-mat.stat-mech↗

arXiv2008

Perfect Cluster States from Imperfect Global Entanglement

The cluster state, the highly entangled state that is the central resource for one-way quantum computing, can be efficiently generated in a variety of physical implementations via global nearest-neighbor interactions. In practice, a systematic phase error is expected in the entangling process, resulting in imperfect cluster states. We present a stochastic measurement technique to generate large perfect cluster states and other graph states with high probability from imperfect cluster states even when their initial entanglement is weak.

quant-ph↗

arXiv2007

One-way quantum computing in optical lattices with many atom addressing

One of the fundamental conditions for one-way quantum computation (1WQC) is the ability to make sequential measurements on isolated qubits that comprise the highly entangled resource for 1WQC, the cluster state. This has been a significant impediment in the implementation of 1WQC with ultracold atoms confined in optical lattices, because the width of the measuring lasers is generally much greater than the atomic (qubit) spacing. We demonstrate that deterministic 1WQC is nevertheless possible, with a polynomial increase in the number of operations, as long as the center of the beams can be positioned with high accuracy. Extending the number of cluster atoms, the scheme is also able to compensate for accidental measurements of an arbitrary number of nearby qubits.

quant-ph↗

arXiv2007

Gaussian potentials facilitate access to quantum Hall states in rotating Bose gases

Through exact numerical diagonalization for small numbers of atoms, we show that it is possible to access quantum Hall states in harmonically confined Bose gases at rotation frequencies well below the centrifugal limit by applying a repulsive Gaussian potential at the trap center. The main idea is to reduce or eliminate the effective trapping frequency in regions where the particle density is appreciable. The critical rotation frequency required to obtain the bosonic Laughlin state can be fixed at an experimentally accessible value by choosing an applied Gaussian whose amplitude increases linearly with the number of atoms while its width increases as the square root.

cond-mat.mes-hall↗

arXiv2006

Validity of the Lowest Landau Level Approximation for Rotating Bose Gases

The energy spectrum for an ultracold rotating Bose gas in a harmonic trap is calculated exactly for small systems, allowing the atoms to occupy several Landau levels. Two vortex-like states and two strongly correlated states (the Pfaffian and Laughlin) are considered in detail. In particular, their critical rotation frequencies and energy gaps are determined as a function of particle number, interaction strength, and the number of Landau levels occupied (up to three). For the vortex-like states, the Lowest Landau level (LLL) approximation is justified only if the interaction strength decreases with the number of particles; nevertheless, the constant of proportionality increases rapidly with the angular momentum per particle. For the strongly correlated states, however, the interaction strength can increase with particle number without violating the LLL condition. The results suggest that in large systems, the Pfaffian and Laughlin states might be stabilized at rotation frequencies below the centrifugal limit for sufficiently large interaction strengths, with energy gaps a significant fraction of the trap energy.

cond-mat.mes-hall↗

arXiv2006

Perfect quantum state transfer with spinor bosons on weighted graphs

A duality between the properties of many spinor bosons on a regular lattice and those of a single particle on a weighted graph reveals that a quantum particle can traverse an infinite hierarchy of networks with perfect probability in polynomial time, even as the number of nodes increases exponentially. The one-dimensional `quantum wire' and the hypercube are special cases in this construction, where the number of spin degrees of freedom is equal to one and the number of particles, respectively. An implementation of near-perfect quantum state transfer across a weighted parallelepiped with ultracold atoms in optical lattices is discussed.

quant-ph↗

arXiv2004

Vortex arrays in a rotating superfluid Fermi gas

The behavior of a dilute two-component superfluid Fermi gas subjected to rotation is investigated within the context of a weak-coupling BCS theory. The microscopic properties at finite temperature are obtained by iterating the Bogoliubov-de Gennes equations to self-consistency. In the model, alkali atoms are strongly confined in quasi-two-dimensional traps produced by a deep one-dimensional optical lattice. The lattice depth significantly enhances the critical transition temperature and the critical rotation frequency at which the superfluidity ceases. As the rotation frequency increases, the triangular vortex arrays become increasingly irregular, indicating a quantum melting transition.

cond-mat.supr-con↗

arXiv2000

Anomalous modes drive vortex dynamics in confined Bose-Einstein condensates

The dynamics of vortices in trapped Bose-Einstein condensates are investigated both analytically and numerically. In axially symmetric traps, the critical rotation frequency for the metastability of an isolated vortex coincides with the largest vortex precession frequency (or anomalous mode) in the Bogoliubov excitation spectrum. As the condensate becomes more elongated, the number of anomalous modes increases. The largest frequency of these modes exceeds both the thermodynamic critical frequency and the nucleation frequency at which vortices are created dynamically. Thus, anomalous modes describe not only the critical rotation frequency for creation of the first vortex in an elongated condensate but also the vortex precession in a single-component spherical condensate.

cond-mat.stat-mech↗

arXiv1999

Nucleation of vortex arrays in rotating anisotropic Bose-Einstein condensates

The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization. This is consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.

cond-mat.stat-mech↗

arXiv1999

Vortex stability of interacting Bose-Einstein condensates confined in anisotropic harmonic traps

Vortex states of weakly-interacting Bose-Einstein condensates confined in three-dimensional rotating harmonic traps are investigated numerically at zero temperature. The ground state in the rotating frame is obtained by propagating the Gross-Pitaevskii equation for the condensate in imaginary time. The total energies between states with and without a vortex are compared, yielding critical rotation frequencies that depend on the anisotropy of the trap and the number of atoms. Vortices displaced from the center of nonrotating traps are found to have long lifetimes for sufficiently large numbers of atoms. The relationship between vortex stability and bound core states is explored.

cond-mat.stat-mech↗

arXiv1998

Beyond the Thomas-Fermi approximation for a trapped condensed Bose-Einstein gas

Corrections to the zero-temperature Thomas-Fermi description of a dilute interacting condensed Bose-Einstein gas confined in an isotropic harmonic trap arise due to the presence of a boundary layer near the condensate surface. Within the Bogoliubov approximation, the various contributions to the ground-state condensate energy all have terms of order R^{-4}ln R and R^{-4}, where R is the number-dependent dimensionless condensate radius in units of the oscillator length. The zero-order hydrodynamic density-fluctuation amplitudes are extended beyond the Thomas-Fermi radius through the boundary layer to provide a uniform description throughout all space. The first-order correction to the excitation frequencies is shown to be of order R^{-4}.

cond-mat.stat-mech↗